Ruth Davidson the first openly gay Tory to stand for the party leadership, opens her campaign. Photograph: David Cheskin/PA/Wire

A contender to become Scotland's next Tory leader has rejected demands for far greater economic powers for the Scottish parliament in an open appeal to traditional Tory voters.

Ruth Davidson, at 32 the youngest of the three candidates and the first openly gay Tory to stand for the party leadership, would draw "a line in the sand" at new powers to give modest control over income tax and borrowing.

That was a "distraction" which would "tie the party in knots" for a year, Davidson said before rejecting the suggestion for more financial autonomy for Scotland, also supported by Fraser.

Portraying herself as the fresh-faced saviour, Davidson said: "Under my leadership, there will be no existential crisis, no wringing of hands. [The] values which made me an instinctive Conservative - that drive my politics - are shared by Scots the length and breadth of the country."

She predicted, however, that it would take a decade before the Tories were strong enough to share power at Holyrood. Her primary objective was to defend the United Kingdom in the run-up to the independence referendum being proposed by the Scottish government.

She described the measures being debated in the Lords to give Holyrood powers over income tax and new £2bn borrowing powers as a one-off "MOT" for the Scottish parliament.

She also dismissed proposals to set a second question on increased financial powers at the referendum.

"I believe that the United Kingdom is a force for good in this world. I believe that we in Scotland walk taller, shout louder and stand stronger for being part of that union," she said, as she became the last of the candidates to launch her campaign.

At the referendum, there would be "no half-way house, no second question, no march to fiscal autonomy. When the referendum is done and Scotland in the union has won the day, let that be an end to it."

Davidson is said to be the candidate most favoured by David Cameron but is the least experienced and least well-known.

Fraser has held a series of prominent party positions, been an MSP for 10 years and is deputy leader at the Scottish parliament.

Jackson Carlaw, the other contender, is seen as the most right-wing and traditional. Twice elected deputy chairman of the Scottish party and a list MSP since 2007, he has a strong base in the west of Scotland party but is seen by senior party figures as too reactionary to suit modern Scottish voters.

Davidson, a former BBC journalist and Territorial Army officer, has a female life partner was elected to Holyrood in May on the party list for Glasgow. She has attracted the fewest well-known supporters, besides John Lamont, one of the few Tories to win a constituency seat outright in May.

She said she was the only candidate who can present herself as one of a new generation of Tories who could convince Scottish voters to rejoin the party.

Younger voters knew little and cared little about Margaret Thatcher's premiership, a period many Tories concede destroyed the party's reputation in Scotland.

After losing every Westminster seat in 1997, the Scottish Tories have had only one MP for the last three elections. In Scotland it lost two seats at the May Holyrood elections, bringing their numbers down to 15.

"There's not just one but two generations of voters after me who have no knowledge of Margaret Thatcher ... Scotland has moved on. The Scottish Conservative party has moved on," she said.